Precision neutral current asymmetry parameter measurements from the Tau polarization at LEP

Measurements of the \(\tau\) lepton polarization and forward-backward polarization asymmetry near the Z\(^0\) resonance using the OPAL detector are described. The measurements are based on analyses of \(\tau \rightarrow{\rm e} \nu_e\nu_{\tau}, \tau\rightarrow \mu\nu_{\mu}\nu_{\tau}, \tau\rightarrow \pi\nu_{\tau}, \tau \rightarrow \rho\nu_{\tau}\) and \(\tau\rightarrow{\rm a}_1\nu_{\tau}\) decays from a sample of 144,810 \(\rm e^+e^-\rightarrow \tau^+\tau^-\) candidates corresponding to an integrated luminosity of 151 pb\(^{-1}\). Assuming that the \(\tau\) lepton decays according to V–A theory, we measure the average \(\tau\) polarization near \(\sqrt{s} ={\rm M}_{\mathrm{Z}}\) to be \(\langle P_{\tau}\rangle= (-14.10 \pm 0.73 \pm 0.55)\%\) and the \(\tau\) polarization forward-backward asymmetry to be \(\rm A_{\mathrm{pol}}^{\mathrm{FB}} = (-10.55 \pm 0.76 \pm 0.25)\%\), where the first error is statistical and the second systematic. Taking into account the small effects of the photon propagator, photon-Z\(^0\) interference and photonic radiative corrections, these results can be expressed in terms of the lepton neutral current asymmetry parameters: